Magnetic resonance imaging (“MRI”) collects data in the Fourier domain, typically referred to as k-space, from the magnetic signals of protons precessing in a magnetic field. The spin frequency, also referred to as the resonance frequency, is a function of a material's gyromagnetic ratio and the strength of the magnetic field. In order to spatially position the collected signal, MRI systems and methods make an underlying assumption about this spin frequency: that the signal is composed primarily of protons in water. Typically, in the human body, this assumption is valid; however, protons in fat resonate at a lower frequency than protons in water. This resonance frequency difference is referred to as the chemical shift. When water and fat signals are imaged together, a resulting shift of the fat signal occurs. This frequency change in k-space results in a spatial shift in image space. During frequency encoding, the off resonance fat signal is interpreted to occur at a different spatial location from where the actual signal originated, producing a superposition of two offset images: an image of water and an image of fat response.
The chemical shift artifact (“CSA”) presents a significant barrier to the quantitative MR image analysis of small features, in which the amount of shift is comparable to the dimension of the object. The CSA appears as a “shadowing” effect in the read direction of MR images. This shadowing effect is illustrated in FIG. 1. The resonance frequency of fat is lower than that of water (by approximately 220 Hz given a 1.5 T field). The fat signal is reconstructed with a spatial shift proportional to the B0 field, the field of view (“FOV”) of the image, and the bandwidth used to acquire the signal. For example, given a 1.5 T magnet, a 20 cm FOV, a 256-pixel matrix, and a 20 kHz bandwidth, the resulting shift is 2.81 pixels, or 2.2 mm. Thus, an object composed of a water signal that is approximately 2.2 mm in size may be completely obscured. The borders of objects may also be corrupted by this artifact.
Typically, the resulting CSA corruption is “read through” by radiologists, however, by corrupting the borders between adjacent regions, it foils quantitative measurements of small water signal features surrounded by fat-containing tissue. The magnitude of the shift increases proportionally to the strength of the magnetic field, thus as B0 field strength increases, the artifact's effects may also increase. This shift occurs primarily in the frequency encoding or read-out direction of the image; a secondary effect is present in the slice select direction of the image. Referring to FIG. 1, in the zoomed view (FIG. 1(b)), the CSA on the right leg appears as a void signal, as indicated by the arrow. In the left leg, the CSA appears as a high-intensity region where the fat and water signals superimpose, resulting in increased signal magnitude.
Although the CSA may be useful for diagnostic purposes, such as “fatty liver,” etc., several methods have been proposed to counteract it. These are broadly categorized into two classes: fat saturation or suppression and the Dixon method.
Since its inception in 1984, the Dixon method has received much attention. The Dixon method seeks to remove the effects of the CSA by exploiting the phase relationships caused by the different resonance frequencies to produce two images: one with fat and water in phase and one with opposed phase. By choosing an echo time, TE, based on the chemical shift between fat and water, Dixon collected two images, one composed of fat and water signal in phase, and one with fat and water signals 180 degrees out of phase. The two images are added and subtracted to produce an image of the fat signal and of the water signal. In the following equations:I0=Sfat+SwaterIπ=Sfat−Swater,  (1)I0 is the image collected with fat and water in phase and Iπ is the image collected with fat and water at opposed phases. The fat and water images may be formed from the two images by the following equations:Ifat=(I0+Iπ)/2Iwater=|I0−Iπ|/2.  (2)
Dixon's original paper employed a simple method of addition and subtraction assuming that the only source of phase difference between the two signals was chemical shift. Intensity inhomogeneities, however, confound the two-point method, resulting in errors in the reconstructed images. This problem was addressed by Skinner and Glover and Coombs et al. Lodes et al. suggest the use of three images acquired at θε[−π, 0, π] to calculate the intensity inhomogeneities. This method has been extended to include a correction algorithm that fits a polynomial to the collected phase and performs trend analysis on the phase.
Inhomogeneity correction is a pivotal component of any proposed single-point Dixon method. As used herein, the terms bias or bias field mean the magnetic field inhomogeneities and magnetic susceptibility of the human body that cause spatially varying shading across MRI images. The bias filed affects both the magnitude and the phase of the collected signal. Although the bias field effects have been studied and simulated, in practice the bias field in MRI images is approached by fitting approximations to the field rather than understanding the underlying mechanisms. A substantial body of literature has been centered around intensity bias correction in MRI. Meyer et al. use an LCJ algorithm for intensity bias correction. Several authors use a polynomial fit or thin-plate splines. Non-parametric correction schemes have also shown promise in coping with bias correction. Rather than retrospectively correct the artifact, Schomberg incorporates correction steps in the MRI reconstruction process. Information theory methods and homomorphic unsharp masking have also been applied to the problem. Prima presented a comparison of model-based methods and several authors have coupled segmentation with intensity correction. It is an adaptation of coupled segmentation that forms the core of the fat suppression technique described herein.
In addition to the issues described above, to characterize tissues, the pixel values in two images are typically compared by division for T2*, T2, and diffusion. Although division may cancel some untoward effects, it is still necessary to remove/reduce the influences of surrounding and/or included fat. Fat may affect a plurality of surface voxels in small or thin tissue regions. The CSA moves fat in the slice select and read directions, producing overlap which may be several pixels wide. High bandwidth limits may alleviate this overlap, but increase noise.
Ideally, calculations would provide correct tissue properties (T2*, etc.) at partial volume fractions below a relatively large, critical value, and the correct values for fat at relatively large volume fractions. Because fat and water signal phases may affect results, TE choice may be used to minimize partial volume effects.
Thus what is still needed is a novel algorithm for distinguishing fat and water signals utilizing only one image, provided the correct phase information from the complex image may be accurately estimated. What is also needed is a novel algorithm for the robust estimation of parameters such as T2* that are adjacent to fat.